Question

The value of integral $\int \frac{dx}{x(\ln x{)}^3}$ is
(where $C$ is constant of integration)

• A. $\frac{1}{(\ln x{)}^3}+C$
• B. $-\frac{1}{2(\ln x{)}^2}+C$
• C. $-\frac{1}{3(\ln x{)}^3}+C$
• D. $-\ln \left(x\right)+C$

Answer 1

The correct option is B $-\frac{1}{2(\ln x{)}^2}+C$

Put $\ln x=z\Rightarrow \frac{1}{x}dx=dz$
Now, $I=\int \frac{dz}{z^3}=-\frac{1}{2}\left(\frac{1}{z^2}\right)=\frac{-1}{2(\ln x{)}^2}+C$